An apparatus for processing data includes first execution circuitry, such as an out-of-order processor, and second execution circuitry, such as an in-order processor. The first execution circuitry is of higher performance but uses more energy than the second execution circuitry. Control circuitry switches between the first execution circuitry being active and the second execution circuitry being active. The control circuitry includes prediction circuitry which is configured to predict a predicted identity of a next sequence of program instructions to be executed in dependence upon a most recently executed sequence of program instructions and then in dependence upon this predicted identity to predict a predicted execution target corresponding to whether the next sequence of program instructions should be executed by the first execution circuitry or the second execution circuitry.